I was doing fine with 12.10 but I read that 13.04 took care of a few of the more sluggish aspects of 12.10 so I decided to upgrade.

The installation package seemed significantly less smooth than 12.10- instead of a snappy, smooth experience it had a few graphical bugs and took a LONG time to load, with various pools of unresponsiveness. Regardless, I went through with it.

Now, unless I boot from USB from the BIOS menu, the computer simply does not boot Ubuntu. I re-installed, to no effect. There is just a single flickering | on the top-left. Randomly pressing keys, after the first 7 or so, starts producing system beeps. The system is not completely unresponsive: It turns the screen on-and-off if I press "Ctrl+Alt+Del".

No boot selection screen at all. Literally the most powerless computer interface I've ever handled in my life. It's a blinking carat that beeps or reacts to CAD. I re-downloaded the image on a windows computer and used a different program to burn it to USB. It feels slightly better this time around, but it could be all placebo. Please do tell me how to reinstall grub in case I reach another dead-end.
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user153011Apr 27 '13 at 21:53

There is a bug with the kernel that effects nvidia drivers
You can either upgrade to saucy or use a mainline kernel

I would use a live cd to edit my /boot/grub/grub.cfg file and change every timeout=0 to timeout=10
This way I will have a chance to push keys during boot
This command should get the job done:sudo sed -i 's/timeout=0/timeout=10/' /media/$USER/*/boot/grub/grub.cfg
you will need to mount the partition with /boot on it.